Look at samples of photos similar to what you want to take. Figure out why you like them, and try to duplicate what you can. Learning about how to control your camera will help you a lot.

Learn about shutter speeds. They help you get clear photos, especially when there is movement, or low light levels.

Learn about lens openings. This helps you control how much in focus your foregrounds and backgrounds will be.

Understanding composition will help you make your photos more interesting and pleasing.
Be very thoughtful about what is in your photo and what you want to keep out of it.

Lighting also has a big effect. Observe if the lighting looks good or unflattering. If it looks bad, then move to a different direction or location. Direct sunlight is often too harsh in the middle of the day. Try the shade, or just turn them away from the sun. You can use reflectors to add light.

Posing can be challenging. Study poses from other photos, or poses of the character you will be photographing.

Look at samples of photos similar to what you want to take. Figure out why you like them, and try to duplicate what you can. Learning about how to control your camera will help you a lot.

Learn about shutter speeds. They help you get clear photos, especially when there is movement, or low light levels.

Learn about lens openings. This helps you control how much in focus your foregrounds and backgrounds will be.

Understanding composition will help you make your photos more interesting and pleasing.
Be very thoughtful about what is in your photo and what you want to keep out of it.

Lighting also has a big effect. Observe if the lighting looks good or unflattering. If it looks bad, then move to a different direction or location. Direct sunlight is often too harsh in the middle of the day. Try the shade, or just turn them away from the sun. You can use reflectors to add light.

Posing can be challenging. Study poses from other photos, or poses of the character you will be photographing.

"Good" is a relative quality. So is "budget". If you want the most control and best quality, a DSLR will be a good choice, if you can find what you want for the price you are willing to spend. These cameras give you the option of changing lenses, and they have a wide range of lenses to choose from. If you are willing to look for a used camera, the price could start around $300. New ones tend to start at more than double that price. Most major brands will give you good quality.

Otherwise, you might do fine with a point-and-shoot camera, which you could find used starting around $60, or new for around $150 and up.

"Good" is a relative quality. So is "budget". If you want the most control and best quality, a DSLR will be a good choice, if you can find what you want for the price you are willing to spend. These cameras give you the option of changing lenses, and they have a wide range of lenses to choose from. If you are willing to look for a used camera, the price could start around $300. New ones tend to start at more than double that price. Most major brands will give you good quality.

Otherwise, you might do fine with a point-and-shoot camera, which you could find used starting around $60, or new for around $150 and up.

"Good" is a relative quality. So is "budget". If you want the most control and best quality, a DSLR will be a good choice, if you can find what you want for the price you are willing to spend. These cameras give you the option of changing lenses, and they have a wide range of lenses to choose from. If you are willing to look for a used camera, the price could start around $300. New ones tend to start at more than double that price. Most major brands will give you good quality.

Otherwise, you might do fine with a point-and-shoot camera, which you could find used starting around $60, or new for around $150 and up.

Look at samples of photos similar to what you want to take. Figure out why you like them, and try to duplicate what you can. Learning about how to control your camera will help you a lot.

Learn about shutter speeds. They help you get clear photos, especially when there is movement, or low light levels.

Learn about lens openings. This helps you control how much in focus your foregrounds and backgrounds will be.

Understanding composition will help you make your photos more interesting and pleasing.
Be very thoughtful about what is in your photo and what you want to keep out of it.

Lighting also has a big effect. Observe if the lighting looks good or unflattering. If it looks bad, then move to a different direction or location. Direct sunlight is often too harsh in the middle of the day. Try the shade, or just turn them away from the sun. You can use reflectors to add light.

Posing can be challenging. Study poses from other photos, or poses of the character you will be photographing.

Bruce provides quality advice, as usual.

I might rearrange the ordering, however. In my opinion, the lighting is the most important component of most photographs - especially portraiture. In fact, the very word "photograph" means to write with light. Lighting can really make or break a portrait. The on-camera flash will very rarely give pleasing light - it will always look "flat" and often washed-out. There are instances where you can use it (e.g. for a little bit of fill) but it should almost never be your main source of light.

After that, it's posing and composition, which go hand-in-hand. As part of composing a pleasing portrait, you must pay equal attention to the subject and to the background. Look past the subject; find background elements that will frame the subject well; hide or obscure elements that will be distracting or unpleasant. Posing can be hard; however, cosplay posing can be easy if you have reference material for the character.

If you have a DSLR, get the book Understanding Exposure by Bryan Peterson. Read it, learn it, practice it, read it again. Understand it thoroughly enough that every page of the book feels like simple common sense.

Like Bruce mentions, study other photos that you like. How is the subject posed? What's in the background? Most importantly, where's the light coming from?